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MathGroup Archive 2006

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Re: Plot3D

  • To: mathgroup at smc.vnet.net
  • Subject: [mg65139] Re: Plot3D
  • From: Bill Rowe <readnewsciv at earthlink.net>
  • Date: Wed, 15 Mar 2006 06:30:07 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

On 3/14/06 at 5:59 AM, BoLe79 at gmail.com (Borut Levart) wrote:

>>The surprising thing isn't that the algorithm Mathematica uses gets
>>things wrong occasionally but that it succeeds as often as it does.

>Why is that surprising? Wouldn't just finding min, max, and
>comparing the values do?

No. Consider the following data set.

In[7]:=
data=Flatten at {Table[x^2+0.05 Random[],{x,-1,1,.05}],1000};

If you do

ListPlot[data];

Mathematica shows the parabolic nature of the data by omitting the one anomalous data point, 1000.

If you do,

ListPlot[data, PlotRange->All]

The bulk of the data appears to lie on the x-axis. The parabolic nature of the bulk of the data is totally obscured.

Which is more useful depends on what you need. You could be interested in the general trend which is what Mathematica shows by default. Or the most important information could be the one point that didn't follow the general trend which gets omitted with the default settings.

There is no way to universally know what will be the most interesting portion of any given data set. Hence, it doesn't seem surprising to me Mathematica fails to display what I am interested in at times. What is surprising to me is how often Mathemetica gets it right.
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